Should you decide to work on this problem, you and your advisor need one of the people in subject Y in your home university to take responsibility for finding out if this gadget is known in Y and, should it become necessary, for letting others in Y know that a graduate student is working on the problem and gently asking them not to work on it.

I hope that the mathematical community will develop standards of etiquette such that mathematicians can safely use the Internet to address these kinds of issues without direct personal contacts, but public discussions of research on the Internet is a relatively new development and not enough time has elapsed to develop such standards.

related: when should you say what you know

I was being a bit hyperbolic. Let me clarify: My default assumption is that the advisor suggested a problem she already had a strategy for answering, and gave the student an idea of the strategy. My unscientific opinion is that this is what happens in nearly all cases, and that students who come up with their own problems together with strategies for solving them are exceedingly rare. The amount of intervention required on the part of the advisor obviously varies, and it is impossible in practice for anyone but the advisor or student (and maybe not even them) to really know how much of the thesis is the student's (though of course the student is expected to write all of it). Indeed, the thesis is really is a product of the interaction between advisor and student, and in most cases an attempt to assign (say) a percentage that expresses what portion of the work was done by the student is foolish, just as it would be in any other collaboration.

Bill,

If you regard this (typical) process as academic dishonesty on the part of the advisor, then we are guilty of academic dishonesty on a truly breathtaking scale! What do you propose to do about it?

Best, Storkle

MO already has a good anti-hierarchical, or rather anti-feudal effect in my eyes: it makes people formulate (and even prove, on occasion) those "folk results" and "folk intuitions" that the experts on a given subject all know but never have really written up and published. This slightly levels the field to the advantage of newcomers who want to learn some modern mathematics (by "modern" I mean "not having a definitive and readable textbook written about it yet"; this does not mean anything like "50 years old or younger") without having to (physically) go to its headquarters and attend the right conferences. And potentially even find some good problems to think about without having to become a grad student of some of the relevant professors. When I read your post, quid, I thought this was exactly what you were trying to prevent. I am glad this was a misunderstanding.

In a narrow sense, we are talking about a specific online forum (MO), with certain technical merits and drawbacks. Its design is for question that get answered (definitely), typically in one try. [This is not always the reality, but the design-idea is this.] Not for some back and forth exchanges over extended periods of time that would seem more apt for collaborative work. So from the mere fact that I or somebody is 'against' something on MO, it does not follow the same would be true for other online fora (with different technical details).

However, it is true that I am generally sceptical towards ideas of largish (online) collaboration. However, for sort of the opposite reason you seem to assume. Some people seem to think that such a developpment will result in a more open and/or egalitarian (math research) community. In my opinion if this would really catch on (beyond some experiments) the exact opposite would happen and the community would become more hierarchical; it would become like those sciences with lot of labor-sharing, large labs and so on [disclaimer: my knowledege of other, than math, scientific communities is only anecdotal].

Anyway, if people think this is off-topic, I'll stop commenting on this point.

I think the idea of featured questions is great. Providing incentives to answer harder questions certainly improves the quality of the contributions, and may even lead to collaborations between users. [..] As a matter of fact, MO users do not invest in research. A bit embarrassing, isn't it? [...] But a week is too a short period to think to a hard problem

Or, occassionaly people post problems they know very well are open and seemingly without direct motivation just to give them visibiliy I assume. (And here I do not mean some 'strangers' asking about the Goldach conjecture or there latest personal variantion thereof or something like that; but people knowing very well what they are doing.) If this were 'allowed' (as opposed to being essential against statements in the FAQs) I am pretty sure this would be a lot more frequent and some people would appreciate this.

quid: What do you mean by "[turning MO into] some giant online collaborative research activity"? In how far do you see a tendency towards that?

In that case the advisor responded in a sensible way.

With this there is even a (weak) documentation of priority and people are informed about the situation. Of course, one gave some information away. But I do not know how much this would hurt. The scenario that then others will start massively working on this with the information in hand seems rather unlikely to me.

If there is anyway no progress I do not see the huge problem (it is perhaps some problem but not huge). Presumably (it is to be hoped) the expertise to be/already obtained to work on the one problem can be also be use on some other problem (if ever an answer shold appear) close by.

However, I agree with Andrew that a preemptive measure to minimize the risk of such things is to keep MO close to its orginal purpose, and not turn it (also) into some giant online collaborative research activity, in contrast to what from other discussions it seems some people would consider desirable. From my perspective, one more reason not to go down this road.

As implicitly alluded to by Darij, one annoying thing are public half-done (or quater or still less, or even only announced) projects, in particular when they turn essentially idle. (This applies to everybody not just students; indeed perhaps students, and people in closely related situations, should be the only ones with some 'right' to do this.)

It is general common courtesy in the mathematical community not to work on a problem that a graduate student is working on. I would say this applies to MO as well.

My suggestion for any graduate student who finds him or herself in this position is to get in touch with your advisor immediately and ask him or her to comment on MO, using his or her real name, that a student is working on the problem, and have him or her deal with the issues. This is because your advisor knows more about etiquette in the mathematical community than you do. I don't see how etiquette with MO is any different from etiquette before MO here.

Because MO happens quickly, if your advisor is on vacation, it is acceptable to contact some other senior person you know (either another professor in your department, or, better yet, another person in your area whom you know) to do this commenting.

Don't worry that 24 hours will make a difference. Unless your advisor has been remiss and let you work on a trivial problem, it will take more than a day to generate an answer that will have a real impact on your thesis.

> I thought the default assumption---in the vast majority of cases---was that the advisor gave a problem she already knew how to solve, and that the goal for the student is to show that they know how to write up the advisor's ideas. >

I consider that behavior academic dishonesty on the part of the advisor. A dissertation is presented to the world as original research by the author. Assistance from the advisor is assumed, of course, but the thesis should not be research of the advisor that is written up by the student.

Really? I thought the default assumption---in the vast majority of cases---was that the advisor gave a problem she already knew how to solve, and that the goal for the student is to show that they know how to write up the advisor's ideas.

There are still disadvantages in collaboration outside of your Ph.D. If you have no publications by yourself it could look like you have no ideas of your own and (say) the more senior person on your papers may appear as the "ideas" person and you're their technical typist. This kind of thing can come up when applying for grants, at tenure and promotion cases and such, even getting your first job. If someone applies for a job and all their publications are with their supervisor, that raises a red flag for me.

Basically, for a non-thesis problem then there's very little disadvantage in collaborating whereas for a thesis problem, part of the goal is for the student to show that they can do things by themselves so there there is a cost.

This is another argument for keeping tight rein on speculative questions: if it is perceived that MO is a place to ask broad-ranging questions then it is more likely that questions pertaining to an entire thesis will come up. But if MO is perceived as a place for asking small, focussed questions, then it is much less likely that it will occur.

If I may say so, then I think that Bill's comment (endorsed by Angelo) is particularly simplistic. It's not just about who solves the problem, it's also about how much work it takes to get make that solution work. One could argue that very little in mathematics is truly new and that most of it is simply gathering together pieces already known and adding a little glue. There, the genius is in knowing which pieces to gather and that could take an expert an afternoon but be an entire thesis for a graduate.

The true solution would be some way in which we, the mathematics community, adjusted our evaluation of PhD theses to take into account the existence of the internet.

So if your thesis problem is posed on MO and solved quickly by an expert who saw it, be happy that you did not waste time working on the problem.

Somebody might solve your dissertation problem before you do. It's unfortunate if it happens, but it does happen sometimes. Ideally you'd have enough things going on for your dissertation that having one key problem knocked-out of the mix shouldn't matter. That's something you should talk with your supervisor about.